It probably will not be necessary to feed the fish. Many species can go without food for as long as a week with no ill effects.

An unbreakable container of a size easily handled when it is half-full of water (minnow bucket, ridded container with air holes in the lid) makes a convenient carrier. Or, use a leak-proof plastic bag closed with a rubber band, place it in an outer bag of similar size to prevent accidental leakage, then into a sturdy container, such as a Styrofoam picnic cooler.

The plastic bag/Styrofoam cooler method is advantageous in stabilizing the water temperature for up to 48 hours. When transferring them to the container, remember that fish need air, and fill the container or plastic bag only about one-third full of water. Use the water from the aquarium.
Add the fish (don't overcrowd) and close the top. Open the container or plastic bag every four or five hours to freshen the air supply.

Remove the aquarium accessories; empty and dry the aquarium. Pack carefully, or have the mover pack them for you.

If convenient, take along in a separate container(s) as much of the water removed from the aquarium as you have room for.

Plants and snails from the aquarium can be carried along in plastic bags with a small amount of water.

Fish might become bruised while traveling. Liquid healing agents to put into the water are available at pet shops.

At destination, replace water and fish in the aquarium as soon as possible. Add tap water a little at a time to fill the aquarium to the proper level, letting the fish adjust gradually to the new water.
New water may need treatment before use to neutralize any chemicals it might contain. Neutralizers can be purchased at most pet shops.

If the fish must be moved in the aquarium itself, remove about half the water, the aerator, heater, hood, and anything else that might shift and cause the glass to break. Cover the top with plastic film to keep the water from splashing out. To avoid breakage, take care that the bottom of the aquarium is solidly supported while it is being lifted and moved.
It is advisable to place the aquarium into a corrugated carton and pad it with crushed paper. Wedge the carton in the car so it will not slide during the trip. Replace the aerator immediately upon arrival at destination.